Strong and weak chaos in weakly nonintegrable many-body Hamiltonian systems

Abstract

We study properties of chaos in generic one-dimensional nonlinear Hamiltonian lattices comprised of weakly coupled nonlinear oscillators, by numerical simulations of continuous-time systems and symplectic maps. For small coupling, the measure of chaos is found to be proportional to the coupling strength and lattice length, with the typical maximal Lyapunov exponent being proportional to the square root of coupling. This strong chaos appears as a result of triplet resonances between nearby modes. In addition to strong chaos we observe a weakly chaotic component having much smaller Lyapunov exponent, the measure of which drops approximately as a square of the coupling strength down to smallest couplings we were able to reach. We argue that this weak chaos is linked to the regime of fast Arnold diffusion discussed by Chirikov and Vecheslavov. In disordered lattices of large size we find a subdiffusive spreading of initially localized wave packets over larger and larger number of modes. The relations between the exponent of this spreading and the exponent in the dependence of the fast Arnold diffusion on coupling strength are analyzed. We also trace parallels between the slow spreading of chaos and deterministic rheology.

15 pages, 14 figures

References in corpus (15)

• Destruction of Anderson localization by a weak nonlinearity
• Universal spreading of wavepackets in disordered nonlinear systems
• The crossover from strong to weak chaos for nonlinear waves in disordered systems
• Weak chaos in the disordered nonlinear Schroedinger chain: destruction of Anderson localization by Arnold diffusion
• Compactons and Chaos in Strongly Nonlinear Lattices
• Spreading of wave packets in disordered systems with tunable nonlinearity
• Spreading of waves in nonlinear disordered media
• KAM tori in 1D random discrete nonlinear Schrödinger model?
• Highly nonlinear dynamics in a slowly sedimenting colloidal gel
• Statistics of wave interactions in nonlinear disordered systems
• Scaling of energy spreading in strongly nonlinear disordered lattices
• Spreading in Disordered Lattices with Different Nonlinearities
• Scaling Properties of Weak Chaos in Nonlinear Disordered Lattices
• Poincaré recurrences in Hamiltonian systems with a few degrees of freedom
• Nonlinear delocalization on disordered Stark ladder

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